Localization of normalized solutions for saturable nonlinear Schrodinger equations

被引:0
|
作者
Wang, Xiaoming [1 ]
Wang, Zhi-Qiang [2 ,3 ]
Zhang, Xu [4 ]
机构
[1] Shangrao Normal Univ, Sch Math & Comp Sci, Shangrao 334001, Peoples R China
[2] Fujian Normal Univ, Coll Math & Stat, Fuzhou 350117, Peoples R China
[3] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA
[4] Cent South Univ, Sch Math & Stat, Changsha 410083, Peoples R China
基金
中国国家自然科学基金;
关键词
saturable nonlinear Schrodinger equation; normalized solutions; semiclassical states; local maximum potential; CONCENTRATION-COMPACTNESS PRINCIPLE; POSITIVE BOUND-STATES; STANDING WAVES; SEMICLASSICAL STATES; ORBITAL STABILITY; ELLIPTIC PROBLEMS; NODAL SOLUTIONS; GROUND-STATES; EXISTENCE; CALCULUS;
D O I
10.1007/s11425-022-2052-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we study the existence and concentration behavior of the semiclassical states with L-2-constraints for the following saturable nonlinear Schrodinger equation: -epsilon(2)Delta v + Gamma I(x) + v(2)/1 + I(x) + v(2) v = lambda v for x is an element of R-2. For a negatively large coupling constant Gamma, we show that there exists a family of normalized positive solutions (i.e., with the L-2-constraint) when epsilon is small, which concentrate around local maxima of the intensity function I(x) as epsilon -> 0. We also consider the case where I(x) may tend to -1 at infinity and the existence of multiple solutions. The proof of our results is variational and the novelty of the work lies in the development of a new truncation-type method for the construction of the desired solutions.
引用
收藏
页码:2495 / 2522
页数:28
相关论文
共 50 条